Miracle: Difference between revisions

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| Title = Miracle

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[225/224]], [[1029/1024]] (7-limit); <br /> [[225/224]], [[243/242]], [[385/384]] (11-limit)

| Comma basis = [[225/224]], [[1029/1024]] (7-limit); <br> [[225/224]], [[243/242]], [[385/384]] (11-limit)

| Edo join 1 = 10 | Edo join 2 = 21

| Edo join 1 = 31 | Edo join 2 = 41

| Generator = 15/14 | Generator tuning = 116.7 | Optimization method = CTE

| MOS scales = ~~...~~, [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]

| MOS scales = …, [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]

| Mapping = 1; 6 -7 -2 15

| Pergen = (P8, P5/6)

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Some temperaments have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and other temperaments have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]]~[[49/48]]~[[50/49]]~[[55/54]]~[[56/55]]~[[64/63]] all [[tempered]] together.

See [[Miracle extensions]] for [[13-limit]] and [[17-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.

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=== Norm-based tunings ===

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit ~~Norm~~-based tunings

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings

|-

! rowspan="2" |

@@ Line 3: / Line 3: @@
 | Title = Miracle
 | Subgroups = 2.3.5.7, 2.3.5.7.11
-| Comma basis = [[225/224]], [[1029/1024]] (7-limit); <br /> [[225/224]], [[243/242]], [[385/384]] (11-limit)
+| Comma basis = [[225/224]], [[1029/1024]] (7-limit); <br> [[225/224]], [[243/242]], [[385/384]] (11-limit)
-| Edo join 1 = 10 | Edo join 2 = 21
+| Edo join 1 = 31 | Edo join 2 = 41
 | Generator = 15/14 | Generator tuning = 116.7 | Optimization method = CTE
-| MOS scales = ..., [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]
+| MOS scales = …, [[1L 9s]], [[10L 1s]], [[10L 11s]], [[10L 21s]]
 | Mapping = 1; 6 -7 -2 15
 | Pergen = (P8, P5/6)
@@ Line 19: / Line 19: @@
 Some temperaments have 11/9 as a neutral third, meaning it is exactly half of a 3/2 (tempering out 243/242), and other temperaments have 8/7 as exactly a third of 3/2. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts.
-Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.
+Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]]~[[49/48]]~[[50/49]]~[[55/54]]~[[56/55]]~[[64/63]] all [[tempered]] together.
 See [[Miracle extensions]] for [[13-limit]] and [[17-limit]] extensions. See [[Gamelismic clan #Miracle]] for technical data.
@@ Line 193: / Line 193: @@
 === Norm-based tunings ===
 {| class="wikitable mw-collapsible mw-collapsed"
-|+ style="font-size: 105%; white-space: nowrap;" | 7-limit Norm-based tunings
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
 |-
 ! rowspan="2" |